Abdurrouf, Gancang Saroja, Muhammad Nurhuda
The double-well potential (DWP) is a prevalent mathematical model for systems with 2 force centers, widely applied in quantum physics. Often expressed as a function with multiple parameters, the DWP can exhibit either single-well or double-well behavior depending on these parameters. Within the tunneling regime, optical properties are primarily characterized by the energy difference resulting from energy splitting (ES). Thus, formulating boundary conditions for the DWP and quantifying ES are critical but understudied areas. This research explores the threshold conditions for the existence of DWPs and ES in 2 common classes of symmetric DWPs: The extensively studied Razavy potentials and the more recently introduced Dong potentials. Utilizing quasi-exact solutions for Razavy potentials and the filter method for Dong potentials, we analyze the dependence of ES on DWP parameters. Our findings align well with existing numerical data, eigenfunction analysis and energy difference approaches. This innovative methodology allows for the examination of threshold conditions for higher ES, and provides an opportunity to control ES in DWPs by adjusting structural parameters. © 2025, Walailak University. All rights reserved.
Department of Physics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Indonesia
